Abstract
In this paper, we study a stochastic model with vaccination and treatment to describe the transmission dynamics of tuberculosis. Firstly, by using the stochastic Lyapunov analysis method, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model, then we obtain sufficient conditions for extinction of the diseases. Our work greatly improves the results of Feng and Qiu (2018). Finally, some examples and numerical simulations are introduced to illustrate our theoretical results.
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